Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a (...) few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (shrink)

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age (...) 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded. (shrink)

Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The spatial content of the (...) formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...) reflèteraient une intuition fondamentale, universelle, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d’inspiration aux mathématiciens au fil des siècles. (shrink)

We agree with Nuñez that the Mundurucu do not master the formal propreties of number lines and logarithms, but as the term "intuition" implies, they spontaneously experience a logarithmic mapping of number to space as natural and "feeling right.".

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

Geometrical intuitions spontaneously drive visuo-spatial reasoning in human adults, children and animals. Is their emergence intrinsically linked to visual experience, or does it reflect a core property of cognition shared across sensory modalities? To address this question, we tested the sensitivity of blind-from-birth adults to geometrical-invariants using a haptic deviant-figure detection task. Blind participants spontaneously used many geometric concepts such as parallelism, right angles and geometrical shapes to detect intruders in haptic displays, but experienced difficulties with symmetry and complex spatial (...) transformations. Across items, their performance was highly correlated with that of sighted adults performing the same task in touch (blindfolded) and in vision, as well as with the performances of uneducated preschoolers and Amazonian adults. Our results support the existence of an amodal core-system of geometry that arises independently of visual experience. However, performance at selecting geometric intruders was generally higher in the visual compared to the haptic modality, suggesting that sensory-specific spatial experience may play a role in refining the properties of this core-system of geometry. (shrink)

We argue that Cohen Kadosh & Walsh's (CK&W's) definitions of neural coding and of abstract representations are overly shallow, influenced by classical cognitive psychology views of modularity and seriality of information processing, and incompatible with the current knowledge on principles of neural coding. As they stand, the proposed dichotomies are not very useful heuristic tools to guide our research towards a better understanding of the neural computations underlying the processing of numerical quantity in the parietal cortex.

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...) representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. (shrink)

La connaissances noyau de la géométrie euclidienne est liée au raisonnement déductif et non à la reconnaissance de motifs perceptuels.

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Leibovich et al. opened up an important discussion on the nature and origins of numerosity perception. The authors rightly point out that non-numerical features of stimuli influence this ability. Despite these biases, there is evidence that from birth, humans perceive and represent numerosities, and not just non-numerical quantitative features such as item size, density, and convex hull.

Many psychological scientists and behavioral neuroscientists affirm that “emotion” influences thinking, decision-making, actions, social relationships, well-being, and physical and mental health. Yet there is no consensus on a definition of the word “emotion,” and the present data suggest that it cannot be defined as a unitary concept. Theorists and researchers attribute quite different yet heuristic meanings to “emotion.” They show considerable agreement about emotion activation, functions, and regulation. The central goal of this article is to alert researchers, students, and other (...) consumers of “emotion” research to the multiple meanings or aspects that distinguished scientists attribute to ”emotion,” increase appreciation of its interesting and challenging complexity, and sharpen perspectives on “emotion” and the associated body of literature that is of critical significance to science and society. (shrink)

This article suggests a way to circumvent some of the problems that follow from the lack of consensus on a definition of emotion (Izard, 2010; Kleinginna & Kleinginna, 1981) and emotion regulation (Cole, Martin, & Dennis, 2004) by adopting a conceptual framework based on discrete emotions theory and focusing on specific emotions. Discrete emotions theories assume that neural, affective, and cognitive processes differ across specific emotions and that each emotion has particular motivational and regulatory functions. Thus, efforts at regulation (...) should target the specific dysregulated emotions. The positive effects of emotion regulation are more likely to be optimized when they result from or lead to emotion utilization—the constructive use of the energy of emotion arousal. Effective processes for regulation differ for basic emotions and emotion schemas. This article identifies neural systems that facilitate emotion experiences and emotion regulation processes. It considers the implications of the developmental change from basic emotions to emotion schemas, and also briefly discusses the effects of interventions on changes in emotion knowledge, emotion regulation, and social and emotional competence. (shrink)

In much of his later work, such as Le théâtre des philosophes of 1995, and perhaps most succinctly in his essay “Was Merleau-Ponty on the Move from Husserl to Heidegger?” of 2008, Taminiaux acknowledges the inspiration of Hannah Arendt’s concern for the lifeworld as a realm of shifting appearances and of human heterogeneous plurality and interlocutory political praxis. He traces Arendt’s insights back to Husserl’s late concern for the lifeworld, as well as to Aristotle, insofar as the Stagirite, in disagreement (...) with Plato, recognizes the autonomous intellectual excellence of phronêsis, and also understands tragic drama in its political importance as a mimêsis of action itself and as accomplishing an intrinsic purification of the powerful passions that it arouses, such as pity and terror. As the title of the 2008 essay indicates, and as Taminiaux acknowledges, however, Merleau-Ponty’s thought also plays a major role in this intellectual nexus. (shrink)

This paper explores anthropomorphism in human-animal interactions from the theoretical perspectives of pragmatism and anthropology of communication. Its aim is to challenge the conception of anthropomorphism as the attribution/inference of human properties to a nonhuman animal, i.e. as a special case of the theory of mind, and to articulate and make plausible an alternative conception of anthropomorphism as a situated direct perception of human properties by someone who is engaged in a given situation, and let themselves be affected by the (...) animal. The paper offers an original perspective for in depth ethnographic and empirical studies of anthropomorphism-in-situation. Such studies could bring new insights in the study of how ordinary people make sense of animal’s behaviors in real-life situations. (shrink)

This paper aims to study the perception of color (representations, synesthesia, denominations, uses and classification) in specific writings such as recipe treatises written from 1520 to 1689. These treatises deal with the manufacture and stages of color in various objects (remedies, blushes and mainly gems). They reveals that color is not only an apparent surface but also a sensitive substance, in particular white and red colors. Although color is a principle of unity for diverse materials, it sometimes becomes contradictory when (...) it is associated with variable signified and signifiers, so that color also offers a play on naming: meaning is sometimes clear, sometimes obscure, and in any case mobile (azure, vermilion). The contemporary reader does not perceive color in the same way as the Renaissance craftsman. Finally, as a principle of classification, it shows an imbalance and hierarchy of colors which, while providing structure to recipes: it gives mainly a place of choice to red and its shades. (shrink)

Les céramiques présentées ici proviennent de quatre dépôts scellés sous une maison de Nicosie et vidés en 1948. Ces fosses, au remplissage homogène, contenaient des cruches, des marmites, des poêlons et de la vaisselle de service produits à Chypre, de rares importations anatoliennes ou balkaniques et une belle collection de vaisselle de table de Ligurie, de Toscane, de Vénétie et d’Émilie-Romagne. Cette dernière, bien datée, permet d’attribuer le contenu des dépotoirs au dernier quart du xvie‑première moitié du xviie s. Une (...) ébauche de chronotypologie peut donc être établie pour les céramiques des ateliers de Lapithos, de Nicosie et du Troodos, très mal connues pour cette période. La confrontation des sources écrites, faisant état de la prise de la ville par les Ottomans en 1570 et des années qui suivirent, avec cette exceptionnelle source archéologique montre que la vie quotidienne avait sans doute repris un cours normal dès le début du xviie s. (shrink)

L’exploration archéologique du site de l’Arkipiskopi dans la vieille ville de Nicosie, conduite par Fryni Hadjichristofi et son équipe (Département des Antiquités de Chypre) de 2009 à 2011 puis en 2016, a mis au jour les vestiges d’un puits à roue élévatrice appelé à Chypre αλακάτιν/alakatin et plus habituellement connu dans le monde méditerranéen sous le nom de sakieh. S’il en existe des exemplaires plus anciens dans l’île, c’est la première machine hydraulique à traction animale permettant de puiser l’eau dans (...) un puits profond fouillée à Nicosie pour les époques latine, ottomane et anglaise. Cette étude entend d’abord examiner et interpréter les vestiges de ces structures au regard des informations livrées par des documents d’archives et des récits de voyageurs, des dessins de la fin du xvie et du début du xviiie siècle, un plan de 1882 et le cadastre de 1948, afin d’en mieux saisir les contextes de fonctionnement sur une longue durée. Elle présente aussi les godets de terre fixés sur la roue pour le puisage de l’eau et qui, à de rares exceptions, ont complètement échappé aux études céramologiques conduites dans l’île. (shrink)

« Amours anfractueuses, revenez,Déchirez le corps clairvoyant.La lumière affectionne les lèvres éclatées. »Jacques Dupin(Le Corps clairvoyant, 1999, p. 86) Quand on parle du corps, on recourt au blasonnement : des morceaux de corps épars donnent à voir un corps fragmenté, en archipel. Une image unitaire/relationnelle du corps semble contrebalancée par sa dimension osirienne/« archipélagique ». Un imaginaire du démembrement hante la tradition poétique qui depuis le xvie siècle s’attarde, conte...

Le dégagement de cinq fosses dépotoirs au comblement homogène sur le site de l’Archipiskopi à Nicosie fouillé par F. Hadjichristofi (Département des Antiquités de Chypre) de 2009 à 2011 a livré un bel échantillonnage de productions chypriotes déjà connues et d’importations byzantines et proche-orientales. Cependant, l’intérêt majeur de ces assemblages réside dans la mise en évidence d’une production locale de poterie à pâte calcaire, glaçurée ou non. Cette activité potière à Nicosie a débuté à la fin du xiie‑xiiie siècle et (...) s’est poursuivie presque inchangée au xive siècle. Les productions de la capitale des Lusignan sont diversifiées et, pour une partie d’entre elles, témoignent d’apports proche-orientaux – émail, bases à disque, cruche à filtre. L’artisanat de la terre dans l’île ainsi que les liens entretenus avec les territoires croisé et musulman du Proche‑Orient sont donc réexaminés au regard de ces nouvelles données. (shrink)

L’article étudie comment l’humain peut être défini dans les rapports créés dans l’imaginaire entre le corps et l’alimentation. En s’appuyant sur des traités de médecine et de cuisine du Moyen Âge au xviie siècle, des essais d’humanistes et les travaux d’anthropologues, d’historiens et de sociologues contemporains, on découvre comment l’acte même de manger permet de définir et construire les frontières du corps humain et un imaginaire de l’alimentation : la nomination de l’aliment et la charge sémantique des métaphores empruntés à (...) l’alimentation définissent une éthique de l’humain et sa vision du corps humain et animal. Une approche médicale complète cette étude linguistique et montre que le fonctionnement des limites extérieures et internes du corps humain se modèle sur la représentation de l’aliment et de ses effets paradoxaux, bénéfiques et pathologiques. Enfin, le corps social du mangeur est délimité par la distance qui le sépare de l’aliment et le lieu assigné à l’animal destiné à être mangé. (shrink)

Depuis la parution de son premier fascicule en 1877, le Bulletin de Correspondance Hellénique joue son rôle de passeur du savoir en faisant connaître à une vaste communauté de chercheurs les résultats des explorations archéologiques qui, dans le monde grec, dans les Balkans, à Chypre, renouvellent les connaissances par l’apport de documents inédits ou réinterprétés. Enraciné dans l’institution qui le publie, l’École française d’Athènes, il n’a cessé d’évoluer avec elle pour être toujours mieu...

S'intéresser au concept de 'catégorie' dans la philosophie d'Aristote c'est se pencher sur l'un des objets qui a le plus suscité de commentaires depuis l'Antiquité jusqu'à la modernité récente -- de Porphyre à Derrida en passant par les stoïciens, Alexandre et les philosophes arabes. Loin d'être limitée au traité qui a porté ce titre ("Des catégories"), traité dont l'objet et le sens même font difficulté, la kategoria se situe à la croisée des divers champs de questionnements philosophiques aristotéliciens et des (...) enjeux de la physique, de la logique, de la dialectique et de la science 'première'. L'objet de ce volume est d'éclairer, à partir de quelques-unes des lectures actuelles et des grandes approches interprétatives, les difficultés majeures d'interprétation que le concept de 'catégorie' (kategoria) a posé à la tradition, ainsi que d'en renouveler la compréhension à même les textes." -- Back cover. (shrink)

Depuis la parution de son premier fascicule en 1877, le Bulletin de Correspondance Hellénique joue son rôle de passeur du savoir en faisant connaître à une vaste communauté de chercheurs les résultats des explorations archéologiques qui, dans le monde grec, dans les Balkans, à Chypre, renouvellent les connaissances par l’apport de documents inédits ou réinterprétés. Enraciné dans l’institution qui le publie, l’École française d’Athènes, il n’a cessé d’évoluer avec elle pour être toujours mieu...

De Berlioz à Gérard Grisey, de Nietzsche à Jankélévitch, ce livre aborde différentes facettes de la création musicale d'un point de vue philosophique et tente de montrer que la musique sécrète un potentiel de transformation précieux à bien des égards: transformation du réel tel qu'il existe, transformation du monde sonore, transformation de l'écoute. Écrire de la musique, l'interpréter, l'écouter, l'apprécier constituent les différents chapitres de cet ouvrage. S'y insèrent des entretiens avec des acteurs de la scène contemporaine: les compositeurs Philippe (...) Leroux, Jean-Luc Hervé, Mauro Lanza, la chanteuse Donatienne Michel-Dansac, le violoncelliste Pierre Morlet et le percussionniste Jean Geoffroy; ces entretiens poursuivent la réflexion qui les précède et la rendent ainsi plus conrète. Au fil des pages, il apparaît qu'une oeuvre musicale, inscrite dans la durée, permet de s'émanciper de l'hégémonie d'une instantanéité et d'une ubiquité virtuelle propres à notre époque. Pour paraphraser Luigi Nono, réveiller l'oreille, c'est en somme réveiller l'homme"--Back cover. (shrink)

Compromises are arrived at when, in spite of the efforts of those participating to mediate and defend their position in a rationally acceptable manner, each remains with his judgment while, at the same time, a decision must be made without further delay. What this means is that the parties agree to an option about which they are not, in their heart of hearts, entirely convinced. This article examines the notion of moral compromise, concentrating thereby on the case of political praxis. (...) It asks whether, in view of the complexity and multiplicity of morally relevant decisions encountered in a pluralist society, it is at all realistic to expect much else from political institutions than what Rawls dismissively refers to as a modus vivendi and whether a conception of justice that is true or reasonable only given the reasonable pluralism of comprehensive doctrines is still a conception of justice, and not simply a compromise between the contending doctrines. (shrink)

This article clarifies my current and seemingly ever-changing position on issues relating to emotions. The position derives from my differential emotions theory and it changes with new empirical findings and with insights from my own and others’ thinking and writing. The theory distinguishes between first-order emotions and emotion schemas. For example, it proposes that first-order negative emotions are attributable mainly to infants and young children in distress and to older individuals in emergency or highly challenging situations. Emotion schemas are defined (...) as emotion feelings interacting with cognition in motivating the decision making and actions of everyday life. (shrink)

Based on hierarchical classification and logistic regression of early US and French COVID-19 clinical trials we show that despite the registration of a large number of trials, only a minority had characteristics usually associated with providing robust and relevant evidence.

Cette étude poursuit des recherches consacrées à une conception originale de la liberté issue pour l’essentiel des stoïciens et de Paul et qui connaît un regain d’intérêt au XVIIe siècle : la liberté comme usage du monde. Il s’agit de voir plus précisément comment Fénelon, se saisissant de la formule de Paul « user du monde comme n’en usant pas », s’efforce de l’approprier à la doctrine du pur amour. Or à l’examen d’une telle entreprise, l’on constate que sa volonté (...) d’interpréter la proposition paulinienne dans une perspective mystique menace la possibilité même d’y répondre. (shrink)